Bound states of spatially separated electrons in crossed electric and magnetic fields

A new mechanism is proposed for the binding of two carriers of the same sign in a two-layer system in crossed electric E and magnetic B fields of a special form. A field configuration for which the electric and magnetic fields in the layers are equal in magnitude and opposite in direction is considered. In this geometry of the fields an additional integral of the motion arises: the pair momentum P. For the case when the masses of the carriers in the layers are considerably different, a method is proposed for calculation the states of a pair without making use of the assumption that the Coulomb interaction between carriers is small. The character of the dependence of the energy of a pair on its momentum, $E(P),$ is determined by the ratio of the fields $|E/B|.$ For $|E/B|⩾Λcr∝e2/ℏc$ the energy of a pair is a monotonic function of $|P|$ and there are no bound states in the system. For $Λ⩽Λcr,$ however, the function $E(P)$ is nonmonotonic. A local maximum and local minimum appear on this function, indicating the appearance of bound states of two carriers of the same sign. The physical mechanism leading to the appearance of bound states in crossed fields is investigated, and their main characteristics are calculated. Ways of realizing these bound states in concrete systems and their possible experimental manifestations are discussed.